Space-charge-limited currents in materials with nonlinear velocity-field relationships

A general parametric form of the current-voltage characteristic of space-charge-limited currents (SCLC) is derived in the virtual cathode approximation. The result is used to obtain several new exact solutions for the trap-free insulator that is characterized by a nonlinear velocity-field (ν - F) relationship. Unlike previously reported results, the new solutions describe the gradual transition from the regime of constant mobility to that of the field-independent drift velocity. The first- and second-order corrections to the Mott-Gurney law then are obtained in a closed form for an important class of velocity-field relationships. Exact solutions are also Obtained for ν - F models that exhibit negative differential mobility behavior. The theory developed in this work is in good agreement with existing experimental data. The general result is used to specify the Condition that allows us to extract the anode field as well as the ν - F dependence from experimental current-voltage characteristics without assuming any a priori ν - F relation. In particular, such extraction is possible for the ideal trap-free insulator or materials with shallow traps. We illustrate the new approach by utilizing available experimental data to extract the ν - F dependence in GaAs.